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1
Set a large pot of water to boil & salt it.
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2
Turn the oven on to its lowest setting; warm 4 pasta bowls in it.
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3
When the water is boiling, add the pasta.
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4
Meanwhile, put 1 tablespoon of the butter and the ham into a medium-size saute pan over medium-high heat.
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5
Cook, shaking pan occasionally, until the ham colors, about 2 minutes, then divide ham among the pasta bowls.
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6
Add remaining butter to the pan and, when the foam subsides, crack the eggs into the pan.
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7
Cook them sunny side up, until the whites are nearly firm & the yolks very runny.
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8
The butter will begin to color while the eggs are cooking; if it threatens to burn, lower the heat to medium.
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9
When the pasta is tender but not mushy, drain it, reserving a bit of the cooking water.
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10
Put the pasta in bowls.
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11
Use a spatula to transfer a fried egg to each bowl of pasta & pour all the butter from the pan around the eggs onto the pasta.
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12
Slice the eggs on the pasta & toss them with the pasta, adding cheese, and if necessary, a little of the pasta cooking liquid, to make a sauce.
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13
Add salt if necessary, & lots of black pepper & serve.
